|By Tom Westbrook and Jane Wardell

SYDNEY (Reuters) - A state premier's desperate move to win re-election by striking an electoral deal with the far-right One Nation party drove a wedge between partners in the ruling coalition on Monday, as Australia's conservative politics faced a lurch to the right.

In an unprecedented move, the Western Australian state leader of the Liberal Party, the senior partner in the governing Liberal-National coalition, agreed on a vote-sharing deal with One Nation at state elections next month.

The deal demonstrated the influence now wielded by One Nation, which advocates protectionism and anti-immigration policies, since its return from 20 years in the political wilderness at national elections last year.

Western Australian state premier Colin Barnett, who is facing defeat in the March 11 election, has agreed to swap preference votes with the state branch of One Nation.

Under Australia's complicated electoral system, voters mark candidates according to preference and the preferences of losing candidates are then redistributed until a winner is determined.

Barnett's deal appeared to split the center-right Liberals and the more conservative Nationals at a national level, another bad sign for embattled Australian Prime Minister Malcolm Turnbull.

Nationals leader and Deputy Prime Minister Barnaby Joyce described the deal as "disappointing" and said Barnett "should seriously consider whether he thinks that this is a good idea".

Coalition colleagues disagreed. Australian Trade Minister Steve Ciobo said the Liberal Party should put itself in the best position to win the Western Australian election.

Industry Minister Arthur Sinodinos, another Liberal, said One Nation, which first rose to prominence under the leadership of Pauline Hanson in the late 1990s with its blatant appeal to white nationalism, was more "sophisticated" now.

Turnbull was left teetering on the brink of a minority government last week when a prominent member of his coalition quit to form a new, more conservative party.

That came as the coalition languished in opinion polls, with support at its lowest in more than a year.

Liberal leader Turnbull is now vulnerable to moves against him from within his own party, just as he toppled previous prime minister Tony Abbott in a party-room coup in September 2015.

Ian Cook, a senior politics lecturer at Perth's Murdoch University, said the deal was another indication of a global trend away from mainstream political parties.

"People are looking around for someone to vote for and in the U.S. they found (President Donald) Trump, because he said he wasn't like the rest," Cook said.

Hanson gained international notoriety 20 years ago when she warned that Australia was in danger of being "swamped by Asians". Her party won significant support in last year's national election with a high-profile campaign that included a call to ban Muslim immigration.